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Perturbative renormalization of composite operators via flow equations. I. (English) Zbl 0755.60100
Summary: We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. We demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive \(\Phi^ 4_ 4\) theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule.

MSC:
60K40 Other physical applications of random processes
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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